Consider a single risk-neutral entrepreneur who has a project that…

Consider a single risk-neutral entrepreneur who has a project that requires an initial investment F at date 0. The entrepreneur knows whether his project is “good” or “bad”, while outsiders only know that the entrepreneur (project) is good with probability v and bad with probability 1 . A good project is completed after one period and generates at date 1 a verifiable cash flow X(G) and private benefits Z(G). These private benefits are non-transferable, i.e., cannot be shared and accrue only to the entrepreneur. A poor project generates zero cash flow at date 1 and can either be terminated or continued. Termination yields verifiable liquidation proceeds L and non-transferable private benefits Z(T) to the entrepreneur. Continuation requires an additional investment F at date 1. If refinanced, the poor project generates at date 2 a verifiable cash flow X(B) and non-transferable private benefits Z(B) to the entrepreneur.

As regards the verifiable cash flows and the non-transferable private benefits of the good and bad project, the following assumptions hold:

2F > X(G) > X(B) > F > L and Z(G) > Z(B) > 0 > Z(T)

There is a single risk-neutral investor (bank) from whom the penniless entrepreneur can obtain financing. Therefore, the bank has all the bargaining power and can make a take-it-or-leave-it offer at date 0. Similarly, if the project turns out to be bad, the bank can unilaterally make the termination/continuation decision (if a project turns out to be bad) and dictate the terms of the refinancing agreement (if the bad project is continued). Instead of financing the project, the bank has the option to invest its funds at a zero return rate, i.e., “store” its funds. There is no discounting, the entrepreneur is protected by limited liability and has an outside option, i.e., not undertaking the project, which yields zero (private) benefits to him.

(a) Suppose the bank provided financing at date 0 and the project does not generate any cash flow at date 1. What is the bank’s return from refinancing and from liquidating?

(b) When (under which conditions) does the bank refinance the bad project? Explain why the bank may refinance the bad project even though 2F > X(B)

(c) Suppose for the remaining parts that the bank prefers refinancing to termination. Anticipating that the bank will refinance the bad project at date 1, which type(s) of entrepreneur would want to obtain funding at date 0? What is the bank’s (date t = 0) expected return?

(d) Under what condition(s) is the bank willing to finance the entrepreneur?

(e) Suppose now that the bank has only limited funds amounting to 2F. As in parts a) to d), the bank can finance at date 0 the single entrepreneur who has either a good or a bad project, as described above. In addition, the bank has at date 1 – but not at date 0 – a further investment option. Besides refinancing a bad project or storing, it can invest F in an alternative project that yields verifiable cash flow X(A) at date 2 with X(A) > X(B). Which type(s) of entrepreneur will want to obtain funding at date 0? What is the bank’s total expected return from investing (both at date 0 and date 1)? Explain.

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